The present invention relates to an optical phased-array that electronically steers a beam of light.
Phased-array is an array of plurality of phase-controlled element. By adjusting the phase relationship among the electromagnetic waves (or other waves such that sonic wave) radiated from each phase-controlled element, the electromagnetic waves radiated from each phase-controlled element become in-phase in a given direction (or at a give position), thus, a constructive interference is formed, and therefore, the phase-array produces a high intensity beam in that direction. In other directions, the electromagnetic waves from each phase-controlled element do not meet the in-phase condition, and are cancelled out with each other due to the interference, therefore, the radiation from the phased-array is close to zero. The geometric dimension of the phased-array (i.e. the aperture) determines the resolution of the phased-array (i.e. the width of the beam). The number of the phase-controlled element is related to the intensity of the beam. The significant advantage of a phased-array device is that the phase relationship among the electromagnetic waves radiated from each phase-controlled element can be adjusted electronically, therefore, the beam can be steered at extremely high speed.
For the prior art, to ensure that the phased-array radiates only one high intensity beam in the given direction, and that the radiation in other directions is close to zero, the distance between the phase-controlled elements (i.e. the center-to-center distance of the adjacent phase-controlled elements) must be less than half of the wavelength for which the phased-array is concerned (details will be in the following).
It is well known that light is also an electromagnetic wave. In the frequency range of light, the wavelength of the visible light is around 0.4 to 0.7 micrometer, the wavelength of infrared is around 0.7 to several hundreds micrometer, and the wavelength of the ultraviolet is around 0.4 to 0.04 micrometer. Now, let""s use the 0.5 micrometer wavelength visible light as an example in the discussion of the prior optical phased-array technology. As mentioned above, to ensure that the phased-array radiates only one high intensity beam in the given direction while the intensity of the radiation is close to zero in other directions, the center-to-center distance between the phase-controlled elements has to be less than 0.25 micrometer. Thus, the size of the phase-controlled element itself must also be less than 0.25 micrometer. At present, the light source as the phase-controlled element, which is phase controllable, and is small enough in size does not exist yet. Therefore, the phased-array in optical frequency is to use a coherent beam passing through many space-phase-modulators to create many beams with particular phase relationship among them, i.e. each phase-modulator produces one beam with a given phase. Here, each phase-modulator is one phase-controlled element as mentioned above. Phase-modulator consists of two electrodes and electro-optical material between the two electrodes. The refractive index of the electro-optical material can be alerted in a certain rang according to the electrical field between the two electrodes, which alerts the optical path length as a beam of light travel trough the phase modulator, and therefore results phase modulation (i.e. phase shifting). The electrical field between the two electrodes is controlled by adjusting the electrical potential on the two electrodes with a controller.
For the sack of the convenience, in this document, when the structure of the phased-array and phase-controlled element are concerned, width means the dimension in the direction perpendicular to the boresight of the phased-array (or simply called as dimension), the thickness means the dimension along the boresight of the phased-array.
Referring now to FIG. 1, a cross-section view of a prior art optical phased-array device. It consists of a controller 11 and an array of optical phase-modulators 12 (it will be called as array of phase-modulators in the following text for simplicity). The array of phase-modulators consists of plurality of phase-modulators. Since the electro-optical material 13 is the liquid-crystal, the phase-modulator array 12 possesses also a front window 14 and a rear window 15. Window 14 and window 15 are usually flat plates, and parallel to each other. They are transparent in the optical frequency rang that they are working with. Each phase-modulator has a control electrode, denoted as 170, 171, . . . , 179, collectively referred as control electrodes 17. Phase-modulator consists of control electrode 17, common electrode 16 and liquid-crystal 13. Common electrode 16 and control electrode 17 are transparent in optical frequency range concerned. FIG. 1 illustrates the cross-section view of a one dimensional phase-modulator array. Control electrode 17 are plurality of parallel strip electrodes. The width of the strip electrode is denoted as w. The spacing between the electrodes is denoted as p. The center-to-center distance between adjacent electrodes is denoted as d. d=p+w. The incident light 18 enters the phase-modulator array 12 from the rear window 15. Light is phase-modulated by each modulator, and the emitted light from each modulator becomes in-phase in direction xcex8, thus, a beam 19 is generated in direction xcex8. The 46 represents the wavefront. The control lines 20, between the phase-modulator array 12 and controller 11 is for carrying the control signal. The prior art requires that the center-to-center distance d to be less than the wavelength in order to ensure that the phased-array produces only one beam in the given direction. Otherwise, there will be other beams in other direction also, which is not desirable. Therefore, prior art has to limit the width of the phase-modulator w (FIG. 1) to be less than the wavelength. Because of this, it produces the following problems:
1. For a give aperture of a phased-array, since the phase-modulator is very small, the required number of the phase-modulator will be very large. For example, for the wavelength of 0.5 micrometer, 20,000 rows of phase-modulator will be needed for each center meter aperture. This makes the structure of the phased-array device very complex, cost, and difficult to fabricate.
2. The spacing p between the electrodes is limited by the insulation requirement and fabrication process. For a given material and fabrication technology, the minimum p achievable can be regarded as a constant. Obviously, the smaller the width of the phase-modulator w, the larger the portion of the aperture that is occupied by the spacing, and therefore, the lower the filling rate. For example, at wavelength of 0.5 micrometer, assuming w and p are all 0.5 micrometer, then 50% of the aperture area is wasted, only half of the incident light is useful.
3. When the dimension of the phase-modulator (i.e. w. Same in the following) is very small, the light entering the phase-modulator significantly diverges due to diffraction, part of the light will enter neighboring phase modulators, which disturbs the light emitted from each phase-modulator, and only a part of light emitted actually possesses the correct phase. Since the thickness of the phase-modulator is much large than the width (e.g. the thickness is larger than 10 xcexcm), the diverging of the light due to diffraction is very significant.
4. When the dimension of the phase-modulator is very small, the width of the electrode is also very small. Since the thickness of the phase-modulator is much larger than its width, i.e. the distance between the electrodes are much larger than the width of the electrode itself, the infringing effect will significantly affect the uniformity of the electrical field within the phase-modulator. Besides, since the distance between the electrodes is much larger than the width of the electrodes, the electrical field of neighboring phase-modulators also interferes with each other significantly. Even if not taking count the disturb from the diverging light of neighboring phase-modulator, the effect due to infringing electrical field would be significant enough to cause phase error in the light travel through each phase modulator.
The above four issues are the existing problems of the prior art. The first and second problem are related to the fabrication cost and the performance, while the third and forth problems are the fundamental issues of the prior art. Because of these, so far, there is no practical optical phased-array device in the market.
Now, let""s analyze the reason that the distance between phase-controlled elements has faced the limitation in the prior art. FIG. 2 illustrates a phased-array of eight phase-controlled elements, 210-217, collectively referred as 21. The light with given phase emits from each phase-controlled element. For simplicity, each phase-controlled element is assumed to be a point source of light. If the light from each point source of light are all in-phase in the direction xcex8, therefore form a constructive interference, it is said xe2x80x9cthe phased-array produces a beam of light in the xcex8 directionxe2x80x9d. In FIG. 2, that beam of light is denoted as 19xcex8. The distance between adjacent point source of light is denoted as d1, d2, . . . , d7. The optical retardation in the xcex8 direction is denoted as xcex41, xcex42, . . . , xcex47. From the geometrical relationship, the followings are obtained:
xcex41=d1 sin xcex8xe2x80x83xe2x80x83(1.1)
xcex42=d2 sin xcex8xe2x80x83xe2x80x83(1.2)
xcex47=d7 sin xcex8xe2x80x83xe2x80x83(1.3)
In order to make the light from each point source of light all in-phase in xcex8 direction, it is necessary to adjust the phase of the light from each point source of light to compensate the optical retardation mentioned above. Therefore, the phase of the light from each point source of light must satisfy the following relationship:
The phase of 211 is ahead of 210 by xcex41 (2xcfx80/xcex),
The phase of 212 is ahead of 211 by xcex42 (2xcfx80/xcex),
xe2x80x83The phase of 217 is ahead of 217 by xcex47 (2xcfx80/xcex),
where, xcex is the wavelength of the light. Taking into account the periodicity of the wave, shifting the phase by an integer number of 2xcfx80 do not make any difference. For example, denoting xcex41 (2xcfx80/xcex)=k1(2xcfx80)+xcfx891, where k1 is an integer. Whether shifting the phase by k1(2xcfx80)+xcfx891 or by xcfx891, the effect is the same. Therefore, in practice, the phase shifting is always determined according to xcfx891 rather k1(2xcfx80)+xcfx891. In this document, when the phase shifting is mentioned, it always means that the 2xcfx80 phase rest has been taken into account unless otherwise explicitly declared.
Now, let""s consider the possibility that the light from each phase-controlled element are also in-phase in other directions. To answer this question, let""s analyze the array illustrated in FIG. 3. This array is same with the array in FIG. 2. Assuming the direction xcex3 which is different from direction xcex8, and denote optical retardation of the light from each phase-controlled element in the direction xcex3 as xcex11, xcex12, . . . , xcex17. From the geometry relationship, we have:
xcex11=d1 sin xcex3,xe2x80x83xe2x80x83(2.1)
xcex12=d2 sin xcex3,xe2x80x83xe2x80x83(2.2)
xcex17=d7 sin xcex3.xe2x80x83xe2x80x83(2.3)
The phase difference of the light from each phase-controlled element in direction xcex3 is denoted as xcfx861, xcfx862 , . . . , xcfx867. They contain two parts: One is the original phase difference among the point source of light (i.e. the phase shifting that has been implemented in order to achieve all the light in-phase in the direction xcex8); another is the phase difference due to the optical retardation in direction xcex3. Therefore, the phase difference between adjacent phase-controlled elements in direction xcex3 is as the following:
xcfx861=xcex41 (2xcfx80/xcex)xe2x88x92xcex11 (2xcfx80/xcex),xe2x80x83xe2x80x83(3.1)
xcfx862=xcex42 (2xcfx80/xcex)xe2x88x92xcex12 (2xcfx80/xcex),xe2x80x83xe2x80x83(3.2)
xe2x80x83xcfx867=xcex47 (2xcfx80/xcex)xe2x88x92xcex17 (2xcfx80/xcex).xe2x80x83xe2x80x83(3.3)
Or rewriting as:
xcfx861=d1 (sin xcex8xe2x88x92sin xcex3)(2xcfx80/xcex),xe2x80x83xe2x80x83(4.1)
xcfx862=d2 (sin xcex8xe2x88x92sin xcex3)(2xcfx80/xcex),xe2x80x83xe2x80x83(4.2)
xcfx867=d7 (sin xcex8xe2x88x92sin xcex3)(2xcfx80/xcex).xe2x80x83xe2x80x83(4.3)
Here, same as before, xcfx861 greater than 0 means the phase of the light from phase-controlled element 211 is ahead of 210 along the direction xcex3, otherwise, means the phase of the light from phase-controlled element 211 is behind of 210 along the direction xcex3. So on for the rest.
The above phase relationship can also be rewritten as:
xcfx862=xcfx861d2/d1,xe2x80x83xe2x80x83(5.1)
xcfx863=xcfx862d3/d2,xe2x80x83xe2x80x83(5.2)
xcfx867=xcfx866d7/d6.xe2x80x83xe2x80x83(5.3)
Only when xcfx861, xcfx862, . . . , xcfx867 are all equal to an integer (including zero) number of 2xcfx80, the light from each phase-controlled element will be all in-phase in direction xcex3. In order to find out if it is possible to have the light from each phase-controlled element to be all in-phase in direction xcex3, now let""s introduce the unknown coefficients n1, n2, . . . , n7, and rewrite the above expressions in the following form:
xcfx861=n1 2xcfx80,xe2x80x83xe2x80x83(6.1)
xe2x80x83xcfx862=n2 2xcfx80,xe2x80x83xe2x80x83(6.2)
xcfx867=n7 2xcfx80.xe2x80x83xe2x80x83(6.3)
The question that whether the light from each phase-controlled element are all in-phase becomes the question that whether n1, n2, . . . , n7 can all be integer.
From (5.1), (6.1) and (6.2), we have:
n2=n1d2/d1,xe2x80x83xe2x80x83(7.1)
Similarly,
n3=n2d3/d2,xe2x80x83xe2x80x83(7.2)
n7=n6d7/d6.xe2x80x83xe2x80x83(7.3)
Assuming for a xcex3, n1 is equal to an integer, from (7.1) to (7.3), it can be seen that unless d1, d2, . . . , d7 are equal to each other, or they have integer number of relationship with each other, n1, n2, . . . , n7 can not all be integer. The prior art phased-array is the regular array, where the phase-controlled elements is equally spaced. d1, d2, . . . , d7 are equal to each other:
d=d1=d2= . . . =d7.xe2x80x83xe2x80x83(8)
Therefore,
xcex4=xcex41=xcex42= . . . =xcex47,xe2x80x83xe2x80x83(9)
xcex1=xcex11=xcex12= . . . =xcex17,xe2x80x83xe2x80x83(10)
xcfx86=xcfx861=xcfx862= . . . =xcfx867,xe2x80x83xe2x80x83(11)
n=n1=n2= . . . =n7.xe2x80x83xe2x80x83(12)
Thus, we can have equation:
sin xcex8=sin xcex3+nxcex/dxe2x80x83xe2x80x83(13)
Therefore, for a regular array, the question of whether the light from each phase-controlled element can all be in-phase becomes the question of whether there is in integer n to satisfy the above equation.
In the following, the discussion will be for the case of 0xe2x89xa6xcex8 less than xcfx80/2 (for the case of xe2x88x92xcfx80/2 less than xcex8 less than 0, the analysis is similar). In FIG. 2 and FIG. 3, if xcex8 greater than 0 corresponds to deflecting light up, then xcex8 less than 0 corresponds to deflecting light down, and xcex8=0 means light beam points the boresight of the phased-array.
When 0xe2x89xa6xcex8 less than xcfx80/2, then 0xe2x89xa6sin xcex8 less than 1, thus,
0 less than sin xcex3+nxcex/d less than 1.
Rewriting it as the following, and call it the xe2x80x9cmain conditionxe2x80x9d:
xe2x88x92nxcex/dxe2x89xa6sin xcex3 less than 1xe2x88x92nxcex/dxe2x80x83xe2x80x83(14)
As mentioned above, whether the light from each phase-controlled element can all be in-phase in direction xcex3 can be determined by if n can be an integer. In the following, we analyze the possibility that n is an integer. For n=0, xcex3=xcex8. This is not consistent with the assumption that xe2x80x9cthe direction xcex3 is different from direction xcex8. Therefore, the case of n=0 will not be considered. In the following, for d=2xcex, d=xcex, d=xcex/2 three cases, we will discuss nxc2x11, nxc2x12, . . . , respectively.
Substituting d=2xcex into (14):
xe2x88x92n/2xe2x89xa6sin xcex3 less than 1xe2x88x92n/2xe2x80x83xe2x80x83(15)
Substituting all possible n values that can satisfy the above equation:
For n=1, (1.5) becomes:
xe2x88x920.5xe2x89xa6sin xcex3 less than 0.5xe2x80x83xe2x80x83(16)
From this, we know that the xcex3 that satisfies (16) is within the range of xe2x88x92xcfx80/6xcx9cxcfx80/6. For xcex3 within this range, the sin xcex8 is in range of 0xcx9c1. Therefore, when output beam from the phased-array is within the range of 0xcx9cxcfx80/2, there is a accompanying beam in the range of xe2x88x92xcfx80/6xcx9cxcfx80/6.
For n=xe2x88x921, (15) becomes:
0.5xe2x89xa6sin xcex3 less than 1.5xe2x80x83xe2x80x83(17)
The xcex3 that can satisfy this condition is in range of xcfx80/6xcx9cxcfx80/2. The corresponding xcex8 is in the range of 0xcx9cxcfx80/6.
For n=2, (15) becomes:
xe2x88x921xe2x89xa6sin xcex3 less than 0xe2x80x83xe2x80x83(18)
The xcex3 that can satisfy this condition is in range of xe2x88x92xcfx80/2xcx9c0. The corresponding xcex8 is in the range of 0xcx9cxcfx80/2.
For n=xe2x88x922, (15) becomes:
1xe2x89xa6sin xcex3 less than 2xe2x80x83xe2x80x83(19)
This condition can be satisfied only when xcex3=xcfx80/2, correspondingly, xcex8=0.
For n=3, (15) becomes:
xe2x88x921.5xe2x89xa6sin xcex3 less than xe2x88x920.5xe2x80x83xe2x80x83(20)
The xcex3 that can satisfy this condition is in range of xe2x88x92xcfx80/2xcx9cxe2x88x92xcfx80/6. The corresponding xcex8 is in the range of xcfx80/6xcx9cxcfx80/2.
Other integer n can not satisfy (14). The results are summarize in following:
n=1, the range of xcex3: xe2x88x92xcfx80/6xcx9cxcfx80/6, the range of xcex8: 0xcx9cxcfx80/2.
n=xe2x88x921, the range of xcex3: xcfx80/6xcx9cxcfx80/2, the range of xcex8: 0xcx9cxcfx80/6.
n=2, the range of xcex3: xe2x88x92xcfx80/2xcx9c0, the range of xcex8: 0xcx9cxcfx80/2.
n=3, the range of xcex3: xe2x88x92xcfx80/2xcx9cxe2x88x92xcfx80/6, the range of xcex8: xcfx80/6xcx9cxcfx80/2.
Therefore, when xcex8 is in the range of 0xcx9cxcfx80/6, there are three accompanying beams. When xcex8 is in the range of xcfx80/6xcx9cxcfx80/2, there are also three accompanying beams. When xcex8=0, there are two accompanying beams. When xcex8=xcfx80/6, there are also two accompanying beams. (In the above, the cases of xcex3=xcfx80/2 or xe2x88x92xcfx80/2 are not taken into account. The same will be for the followings).
Substituting d=xcex into (14):
xe2x80x83xe2x88x92nxe2x89xa6sin xcex less than 1xe2x88x92nxe2x80x83xe2x80x83(21)
Substituting all possible n values into the condition as in the case of d=2xcex. The results are: Only when n=1, there is an accompanying beam. The range of the xcex3 is xe2x88x92xcfx80/2xcx9c0; the range of xcex8 is 0xcx9cxcfx80/2. When xcex8=0, the corresponding xcex3 is xcfx80/2 and xe2x88x92xcfx80/2, and there is just no accompanying beam.
Substituting d=xcex/2 into (14):
xe2x88x922nxe2x89xa6sin xcex3 less than 1xe2x88x922nxe2x80x83xe2x80x83(22)
No matter what integer value of the n is, there is no xcex3 that can satisfy this condition. Therefore, there is no accompanying beam, no matter what range the xcex8 is. However, when xcex8=xcfx80/2, we have n=1, and correspondingly, xcex3=xe2x88x92xcfx80/2. The accompanying beam is just about to occur, but just have not occurred yet. It can be deduced tllat when d greater than xcex/2, there will be accompanying beam.
In above, we have calculated d=2xcex, xcex, xcex/2 three cases. The rule for the occurrence of the accompanying beams is that: the larger the d, the more the accompanying beams; when d is less than xcex/2, there is no accompanying beam.
In practical application, the scanning angular range is often much smaller than xcfx80/2. At that time, the maximum d can be larger than xcex/2 without introducing an accompanying beam. For example:
From (13), take n=1, xcex3=xe2x88x92xcfx80/2 (i.e. the accompanying beam is about to occur but have not occurred yet), for difference scanning angular range, the maximum d is determined as followings:
When xcex8=xe2x88x9230xc2x0xcx9c30xc2x0, d=0.67xcex,
When xcex8=xe2x88x9210xc2x0xcx9c10xc2x0, d=0.85xcex,
When xcex8=xe2x88x925xc2x0xcx9c5xc2x0, d=0.92xcex.
When xcex8=xe2x88x921xc2x0xcx9c1xc2x0, d=0.98xcex.
The above analysis has explained why prior arts require to place the phase-controlled elements in a spacing less than half wavelength or less than one wavelength. If the distance between phase-controlled element is less than the wavelength, then, the dimension of the phased-controlled element itself must be smaller than the wavelength.
In practical application, the maximum d without accompanying beam can be even larger. For example, if limiting the light from each phase-controlled element in the angular range corresponding to the angular range of the scanning of the beam from the phased-array, then, beyond this angular range, even if the condition for accompanying is satisfied, there will still be no accompanying beam. The maximum d can be estimated as following:
From (13), take n=1, xcex3=xe2x88x92xcex8(i.e. the accompanying beam is about to occur but has not occurred yet), for different scanning angular range, the maximum d can be determined. Some examples are listed below:
When xcex8=xe2x88x9230xc2x0xcx9c30xc2x0, d=xcex,
When xcex8=xe2x88x9210xc2x0xcx9c10xc2x0, d=2.8xcex,
When xcex8=xe2x88x925xc2x0xcx9c5xc2x0, d=5.7xcex,
When xcex8=xe2x88x921xc2x0xcx9c1xc2x0, d=28xcex.
In summary, for prior art, there is always a restriction in the distance between the phase-controlled elements by the wavelength. When the distance between the phase-controlled elements is larger than the wavelength, the scanning angular range decreases rapidly as the distance is enlarged.
U.S. Pat. No. 5,093,740 (issued on Mar. 3, 1992) by Dorschner etc. described a liquid-crystal based array of longitudinal phase-modulators, as shown in FIG. 1. This patent also described a sub-array method to reduce the control lines. But this patented technology limited the scanning angle to some special, discrete values. Furthermore, even if the sub-array method is used, its number of control line is still a large number. Therefore, that device does not have much significance in practical application.
Before describing the principle and method of the present invention, let""s briefly describe the sub-array method of prior art. Referring now to FIG. 1. The strip electrodes are grouped, and each group becomes a sub-array. Each sub-array has plurality of phase-modulators. For each phase-modulator at the corresponding position in each sub-array, its control electrode is connected in parallel, and is controlled in parallel by the controller. FIG. 4 describes the phase relationship among the phase-controlled elements in each sub-array and among the sub-arrays. The figure illustrates three adjacent sub-arrays: 301, 302 and 303. In FIG. 4, the horizontal axis represents the geometric position of each phase-modulator, and the stair-like line represents the phase of each phase-modulator. Since in each sub-array, the phase-modulator of the corresponding position is controlled in parallel, the shape of the stair-like line 22 is identical for the three sub-arrays. That is to say that within each sub-array, the light in the given direction is all in-phase. However, the light among the sub-arrays is not necessary to be in-phase in the given direction. The mis-match of the phase among sub-arrays can be illustrated with phase relationship at the boundary between two adjacent sub-arrays, as shown in FIG. 4. In FIG. 4, on the boundary I1,2 of two adjacent sub-arrays 301 and 302, the stair-like line 22 have a phase difference xcex2. In general, xcex2 is not equal to zero or 2xcfx80. On the boundary I2,3, the situation is similar. Therefore, for the prior art, only when the beam of the light is in some special directions such that the xcex2 is happen to be equal to zero or 2xcfx80, the light from each sub-array will become in-phase with each other. In all other directions, xcex2 is not equal to zero or 2xcfx80, the phase of the light from each sub-array does not match with each other, and the phased-array can not work. Therefore, the sub-array technique proposed by Dorschner etc. can only deflect beam to some special discrete angles. This obviously affects its practical applications.
James A. Thomas, Mark Lasher etc. used the cascade of two scanner to solve the problem of phase mis-match among sub-array, referring to xe2x80x9cOptical Scanning Systems: Design and Applicationsxe2x80x9d, Leo Beiser and Stephen F. Sagan, Ed., Proc. SPIE 31, pp.124-132(1997). However, they still did not overcome the problems caused by the limitation of wavelength on the size of phase-controlled element and on the spacing between the phase-controlled elements. These problems include: Scanning angular range is extremely small, and number of scanning lines is less than the number of rows of the phase-controlled elements.
The present invention provides an optical phased-array device. The said device consists of plurality of phase-controlled elements that form an irregular phased-array, and means to control the phase relationship among the light from each phase-controlled element such that to deflect a beam of light in a given direction; the effective position of the phase-controlled elements form an irregular pattern, and the average distance between the adjacent phase-controlled elements is substantially larger than the wavelength of the light.
An optical phased-array device according to the present invention, wherein irregular phased-array consists of plurality of sub-arrays which consists of plurality of phase-controlled elements; the effective positions of the phase-controlled elements of the sub-array form irregular pattern, and the effective array of the sub-arrays are also irregularly arranged with respective to each other.
The present invention also provides method to control sub-arrays, which includes parallel controlling of the sub-arrays and independent controlling of each sub-array. Sub-array controlling method also includes additional phase-modulator for sub-array phase compensation.
An optical phased-array device according to the present invention also includes the array of lenses or mirrors, which are coupled with the phase-modulators; whereby, forming virtual array of point source of light.